Easy Math Problem

Kanari recently worked on perfect numbers.

Perfect numbers are a special kind of natural numbers. A number is a perfect number if and only if the sum of all the true factors (divisors other than itself) is equal to itself. Such as $6=1+2+3$, $28=1+2+4+7+14$, etc.

Kanari made a kind of semi-perfect number of his own according to the definition of perfect number.

Let $S$ be the set of all the true factors of the natural number $X$. If there is a subset of $S$ such that the sum of the numbers in the subset is equal to the number itself, the number is said to be semi-perfect.

Obviously, all perfect numbers are semiperfect numbers. In addition, there are some numbers that are not perfect, and they also belong to Kanari's semi-perfect numbers. For example, the true factors set of $24$ is $\{1,2,3,4,6,8,12\}$, we can select a subset $\{2,4,6,12\}$, meet that $24=2+4+6+12$. So $24$ can be called a semi-perfect number.

Kanari wants to know if he can find an integer $k$ which is a multiple of positive integer $p$, such that $k$ is a semi-perfect number.

Since Kanari is not good at math, he wants the $k$ not to be too large ($k\leq 2\times 10^{18}$), and the size of the subset is not larger than 1000. He wants you to give the subset you select.

This problem contains multiple test cases.

The first line contains a single integer $T$ ($1\leq T\leq 4000$) indicating the number of test cases.

Then $T$ cases follow, each of which contains a single interger $p$ ($1\leq p\leq 10^9$).

Output $2T$ lines.

For each test case, if there is some integer $k$ that satisfy the condition, output two space-separated integers on the first line, $k$ ($k\leq 2\times 10^{18}$) and $n$ ($1 \leq n \leq 1000$) (the size of the subset you select). Then output $n$ space-separated integers on the second line, the subset you select.

If you cannot find such $k$, output "-1" on the first line, and an empty line on the second line.

Please don't output extra space at the end of each line.

2
6
1

48 5
2 4 6 12 24
12 4
1 2 3 6

“红旗杯”第十五届东北地区大学生程序设计竞赛